In this paper we develop a theoretical framework that helps to analyze the role of monetary policy in responding to asset-price bubbles. A large and rapid fall in the nominal price of assets that form the basis of collateral for loans from financial intermediaries can have adverse effects on financial system stability. This asymmetric effect of asset price changes, by reducing the extent of intermediated finance, can reduce output below potential and keep inflation below the central bank's target for extended periods. We demonstrate that there may be circumstances where monetary policy should be tightened in response to an emerging asset=price bubble, in order to burst the bubble before it becomes too large, even though this means that expected inflation is below target in the short run. Such a policy is optimal because it can help to avoid extreme longer-term effects of a larger asset-price bubble and its eventual collapses. In principle, the adverse effects of asset-price bubbles on financial system stability can be moderated through appropriate financial system regulation and supervision. Nevertheless, provided that the effects of asset-price bubbles on the economy are not entirely eliminated, a role for monetary policy may remain.